Atheist VS Naturalist - the latter sounds more appealing to me...

[polymath257]

So, what conflict resolution procedure do you propose for determining the truth or falsity of claims about the supernatural? If two people make conflicting claims about some supernatural topic, how can the dispute be resolved? It seems to me that in order to make truth claims, there has to *at least* be some sort of process to separate truth from falsity. Both math and science have such. What about the study of the supernatural?

It depends on how you're defining "supernatural." If you're defining it as that which is unknowable to humans, I'd say that no truth resolution is possible. Because we can't understand it, we can't make claims about it. We might claim that something which seems supernatural has happened, but this would also be untestable. Because that which is outside of nature -- the only purview of science -- can't be tested by science. 

Some people might dislike the idea of having a part of the world which can't by definition be tested. But we can't always get what we want. 

We went over this. That definition doesn't work for a variety of reasons. I gave examples before.

And like I said, in any particular case, you have to *test* to see if the mathematical formulation fits the data or not. The whole game is in that phrase 'short of other factors involved that may interfere with their interactions or whatever'. You have to *test* to see if there are such 'interactions' and whether you broke things into 'objects' correctly, and whether there is 'conservation of objects'. Once again, the situations where the math does apply are the interesting ones because they are saying there is a conservation law of sorts.

Again, you're not talking about math. You're talking about empirically-known situations which are measured by math. 

I want to know whether a googolplex is really smaller than a googolplex plus one. Do we need an empirical test to determine the truth of this? Or is it known through definitions and logic?

No, it is a result from an axiom system. We make assumptions (the axioms) and derive the result from those axioms.

If we choose different axioms, we get a different collection of results. I can (easily) come up with usable axioms that allow for a googleplex and a googleplex plus one to be equal and where no order consistent with the operations can be defined.

You seem to think there is only one possible mathematics. And that is wrong. You seem to think there is only one 'logic'. And that is also wrong.

It isn't tested empirically *because* it says nothing about the real world. When dealing with the real world, testing is required.